Sequences and Series
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
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Find the sum of first n
terms of the following series:5+11+19+29+41+˙
Find the indicated terms of the sequence whose nthterms are : an=2nn2;a7
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is then sum?
Find the sum of the following APs : (i) 2, 7, 12, . . . , to 10 terms.
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Figure). In how may rows are the 200 logs placed and how many logs are in the top row?
The sum of first three terms of a G.P. is 1213and their product is 1. Find the common ratio and the terms.
Write first four terms of the AP, when the first term a and the common difference d are given as follows:(i) a = 10, d= 10 (ii) a = –2, d = 0 (iii) a = 4, d = – 3 (iv) a = – 1, d = 1/2(v) a = – 1.25, d = – 0.25
If a, b, c and d are in G.P. show that (a2+b2+c2)(b2+c2+d2)=(ab+bc+cd)2.